Despite difficulties in general division, magnitude comparison, and sign detection, residue number system arithmetic has been used for many special-purpose systems in light of its parallelism and modularity for the most common arithmetic operations of addition/subtraction and multiplication. Computation in RNS requires modular reduction, both for the initial conversion from binary to RNS and af...

we present new division algorithms for Residue Number System (RNS). The algorithms are based on a sign estimation procedure that computes the sign of a residue number to be positive, negative, or indeterminate. In the last case, magnitude of the number is guaranteed to be in a limited interval whose size is related to the cost of the sign estimation process. Our division algorithms resemble SRT...

Currently there are design barriers inhibiting the implementation of high-precision digital signal processing (DSP) objects with field programmable logic (FPL) devices. This paper explores overcoming these barriers by fusing together the popular distributed arithmetic (DA) method with the residue number system (RNS) for use in FPL-centric designs. The new design paradigm is studied in the conte...

In this paper we combine the residue number system (RNS) representation and the leakresistant arithmetic on elliptic curves. These two techniques are relevant for implementation of elliptic curve cryptography on embedded devices. It is well known that the RNS multiplication is very efficient whereas the reduction step is costly. Hence, we optimize formulae for basic operations arising in leak-r...

On an embedded device, an implementation of cryptographic operation, like an RSA modular exponentiation [12], can be attacked by side channel analysis. In particular, recent improvements on horizontal power analysis [3,10] render ineffective the usual counter-measures which randomize the data at the very beginning of the computations [4,2]. To counteract horizontal analysis it is necessary to r...

This paper presents a novel architecture for a Residue Number System (RNS) based 1D 5/3 Discrete Wavelet Transform (DWT) implementation by using a combination of Filter Bank (FB) and Lifting Scheme (LS). It is designed to modify the architecture of existing binary lifting scheme based 5/3 DWT and RNS based Filter Bank (FB) 5/3 DWT. In this proposed architecture, non-binary RNS arithmetic operat...

The need for both speed and increased precision in modern digital signal processing (DSP) applications represents a serious implementation obstacle. This paper explores the arithmetic benefits provided by the residue number system (RNS) for the design of such systems. Concretely, the fusion of the RNS with the popular distributed arithmetic (DA) is considered for the implementation of a discret...

An Elliptic Curve Point Multiplier (ECPM) is the main part of all Elliptic Curve Cryptography (ECC) systems and its performance is decisive for the performance of the overall cryptosystem. A VLSI Residue Number System (RNS) architecture of an ECPM is presented in this paper. In the proposed approach, the necessary mathematical conditions that need to be satisfied, in order to replace typical fi...

One of the biggest challenges confronting the bioinformatics community is fast and accurate sequence alignment. The Smith-Waterman algorithm (SWA) is one of the several algorithms used in addressing some of these challenges. Though very sensitive in doing sequence alignment, SWA is not used in real life applications due to the computational cost associated with the software implementation. Heur...

The reverse converter is the most complex and essential part of residue number system (RNS), and has a significant role in the general performance of RNS. Recently, it is showed that the reverse converter performance could be significantly improved using different adder’s type in the architecture of reverse converters, rather than just using one type of adder topology. This technical report aim...